Singularities of Møller-Plesset series: example "o2- aug-cc-pvdz"

Molecule X 1^Sigma+ State of O2-. Basis AUG-CC-PVDZ. Structure ""

Content


ExamplesAr cc-pVDZbh aug-cc-pVQZ 0.9r_ebh aug-cc-pVQZ 1.0r_ebh aug-cc-pVQZ 1.1r_ebh aug-cc-pVQZ 1.2r_ebh aug-cc-pVQZ 1.3r_ebh aug-cc-pVQZ 1.4r_ebh aug-cc-pVQZ 1.5r_ebh aug-cc-pVQZ 1.6r_ebh aug-cc-pVQZ 1.7r_ebh aug-cc-pVQZ 1.8r_ebh aug-cc-pVQZ 1.9r_ebh aug-cc-pVQZ 2.0r_ebh aug-cc-pVQZ 2.1r_ebh aug-cc-pVQZ 2.2r_ebh cc-pvdz 1.5rebh cc-pvdz 2rebh cc-pvdz rebh cc-pvqz 1.5rebh cc-pvqz 2rebh cc-pvqz rebh cc-pvtz 1.5rebh cc-pvtz 2rebh cc-pvtz reh- cc-pv5zh- cc-pvqzhf aug-cc-pVDZ 1.5r_ehf aug-cc-pVDZ 2.0r_ehf aug-cc-pVDZ r_ehf cc-pvdz 1.5rehf cc-pvdz 2rehf cc-pvdz 2rehf cc-pvdz rena-pl aug-cc-pvdzNe cc-pVDZo2- aug-cc-pvdz
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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Quadratic approximants

[n1n2n3] approximant is defined as a solution of the quadratic equation
A(z)f2 +  B(z)f +  C(z) = 0
with polynomial coefficients A(z), B(z) and C(z) of degree n3, n2 and n1 respectively.

Square-root singularities are determined as zeroes of the discriminant
D(z) = B2(z) - 4A(z)C(z).
The weight c of the singularity zc is defined so that
f ~ c(1 - z/zc)1/2 at z -> zc.
The weight is calculated by formula
c = 1/2[-z(D/A2)']1/2
where r. h. s. of the above equation is evaluated at z = zc.

Table 1. Singularities with their weights for the quadratic approximant [5, 5, 4]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5918 + 0.0694 i
0.0738 + 0.372 i
Singularities of quadratic [5, 5, 4] approximant
2
-0.5918 - 0.0694 i
0.0738 - 0.372 i
3
-0.5976
0.358
4
-0.509 + 0.5523 i
0.00852 - 0.0055 i
5
-0.509 - 0.5523 i
0.00852 + 0.0055 i
6
-0.5016 + 0.5829 i
0.00583 + 0.00848 i
7
-0.5016 - 0.5829 i
0.00583 - 0.00848 i
8
1.4941
0.107
9
-1.5098
0.158 i
10
7.5008
9.58 i
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Table 2. Singularities with their weights for the quadratic approximant [5, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.3452
0.0000641
Singularities of quadratic [5, 5, 5] approximant
2
0.3453
0.0000641 i
3
-0.4841 + 0.0164 i
0.0093 + 0.00639 i
4
-0.4841 - 0.0164 i
0.0093 - 0.00639 i
5
-0.5782 + 0.1969 i
0.0225 + 0.0126 i
6
-0.5782 - 0.1969 i
0.0225 - 0.0126 i
7
-0.6505
0.668
8
-0.8653
0.0528 i
9
1.414
0.0546
10
-25.9719
0.457
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Table 3. Singularities with their weights for the quadratic approximant [6, 5, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5687 + 0.0692 i
0.379 + 0.416 i
Singularities of quadratic [6, 5, 5] approximant
2
-0.5687 - 0.0692 i
0.379 - 0.416 i
3
-0.8281
1.97
4
-0.8835
8.19 i
5
-1.4658 + 1.0136 i
0.335 + 0.651 i
6
-1.4658 - 1.0136 i
0.335 - 0.651 i
7
1.8885 + 0.5385 i
0.278 + 0.0219 i
8
1.8885 - 0.5385 i
0.278 - 0.0219 i
9
1.5405 + 1.3706 i
0.0874 - 0.213 i
10
1.5405 - 1.3706 i
0.0874 + 0.213 i
11
3.8427
0.424
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Table 4. Singularities with their weights for the quadratic approximant [6, 6, 5]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5696 + 0.0698 i
0.436 + 0.386 i
Singularities of quadratic [6, 6, 5] approximant
2
-0.5696 - 0.0698 i
0.436 - 0.386 i
3
-0.7764
0.647
4
-0.9641
0.552 i
5
1.5454 + 0.4115 i
0.0909 - 0.107 i
6
1.5454 - 0.4115 i
0.0909 + 0.107 i
7
-1.3203 + 1.2212 i
0.447 + 0.104 i
8
-1.3203 - 1.2212 i
0.447 - 0.104 i
9
2.0455 + 1.0137 i
0.172 + 0.143 i
10
2.0455 - 1.0137 i
0.172 - 0.143 i
11
-1.4415 + 6.3421 i
0.67 + 0.469 i
12
-1.4415 - 6.3421 i
0.67 - 0.469 i
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Table 5. Singularities with their weights for the quadratic approximant [6, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5734 + 0.0706 i
0.671 + 0.209 i
Singularities of quadratic [6, 6, 6] approximant
2
-0.5734 - 0.0706 i
0.671 - 0.209 i
3
-0.7177
0.335
4
1.2516
0.0116
5
-1.2964
0.116 i
6
1.2896 + 0.6064 i
0.0106 + 0.0255 i
7
1.2896 - 0.6064 i
0.0106 - 0.0255 i
8
-1.6548
0.176
9
1.6722
0.0089 i
10
1.767
0.0116
11
-1.2203 + 1.3043 i
0.156 - 0.223 i
12
-1.2203 - 1.3043 i
0.156 + 0.223 i
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Table 6. Singularities with their weights for the quadratic approximant [7, 6, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5667 + 0.0695 i
0.259 + 0.408 i
Singularities of quadratic [7, 6, 6] approximant
2
-0.5667 - 0.0695 i
0.259 - 0.408 i
3
-0.7729 + 0.0998 i
0.0316 - 0.261 i
4
-0.7729 - 0.0998 i
0.0316 + 0.261 i
5
-0.8924
0.195
6
-1.1718
0.591 i
7
-1.3778 + 0.8834 i
0.197 - 0.621 i
8
-1.3778 - 0.8834 i
0.197 + 0.621 i
9
1.5928 + 0.4795 i
0.118 - 0.0462 i
10
1.5928 - 0.4795 i
0.118 + 0.0462 i
11
1.7574 + 1.3453 i
0.0374 - 0.19 i
12
1.7574 - 1.3453 i
0.0374 + 0.19 i
13
44.728
4.03
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Table 7. Singularities with their weights for the quadratic approximant [7, 7, 6]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5716 + 0.0741 i
0.451 + 0.13 i
Singularities of quadratic [7, 7, 6] approximant
2
-0.5716 - 0.0741 i
0.451 - 0.13 i
3
-0.6312
0.639
4
-0.6788
0.547 i
5
-0.8665 + 0.1295 i
0.289 + 0.169 i
6
-0.8665 - 0.1295 i
0.289 - 0.169 i
7
1.6247 + 0.4484 i
0.139 - 0.125 i
8
1.6247 - 0.4484 i
0.139 + 0.125 i
9
-1.3744 + 1.0876 i
0.349 + 0.315 i
10
-1.3744 - 1.0876 i
0.349 - 0.315 i
11
1.8228 + 1.1486 i
0.119 + 0.206 i
12
1.8228 - 1.1486 i
0.119 - 0.206 i
13
4.8696 + 10.6601 i
0.973 + 0.0647 i
14
4.8696 - 10.6601 i
0.973 - 0.0647 i
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Table 8. Singularities with their weights for the quadratic approximant [7, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5684 + 0.0702 i
0.358 + 0.379 i
Singularities of quadratic [7, 7, 7] approximant
2
-0.5684 - 0.0702 i
0.358 - 0.379 i
3
-0.7783
1.03
4
-0.9657
0.186 i
5
-1.0488 + 0.1503 i
0.154 + 0.0905 i
6
-1.0488 - 0.1503 i
0.154 - 0.0905 i
7
-1.2801 + 0.8612 i
0.0373 - 0.269 i
8
-1.2801 - 0.8612 i
0.0373 + 0.269 i
9
1.5625 + 0.4638 i
0.0981 - 0.042 i
10
1.5625 - 0.4638 i
0.0981 + 0.042 i
11
1.7611 + 1.4954 i
0.0535 - 0.157 i
12
1.7611 - 1.4954 i
0.0535 + 0.157 i
13
0.2968 + 3.9526 i
0.03 + 0.329 i
14
0.2968 - 3.9526 i
0.03 - 0.329 i
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Table 9. Singularities with their weights for the quadratic approximant [8, 7, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5688 + 0.0703 i
0.384 + 0.378 i
Singularities of quadratic [8, 7, 7] approximant
2
-0.5688 - 0.0703 i
0.384 - 0.378 i
3
-0.767
1.43
4
-0.8174
1.36 i
5
-0.9278 + 0.0666 i
0.586 + 0.63 i
6
-0.9278 - 0.0666 i
0.586 - 0.63 i
7
1.3259 + 0.0093 i
0.0335 - 0.0356 i
8
1.3259 - 0.0093 i
0.0335 + 0.0356 i
9
-1.3953 + 0.9381 i
0.0902 + 0.617 i
10
-1.3953 - 0.9381 i
0.0902 - 0.617 i
11
1.6455 + 0.504 i
0.159 + 0.0000232 i
12
1.6455 - 0.504 i
0.159 - 0.0000232 i
13
1.765 + 1.415 i
0.0978 - 0.234 i
14
1.765 - 1.415 i
0.0978 + 0.234 i
15
14.7294
1.44
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Table 10. Singularities with their weights for the quadratic approximant [8, 8, 7]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5688 + 0.0704 i
0.38 + 0.366 i
Singularities of quadratic [8, 8, 7] approximant
2
-0.5688 - 0.0704 i
0.38 - 0.366 i
3
-0.7516
0.659
4
-0.9301
0.19 i
5
-0.9428 + 0.158 i
0.226 + 0.067 i
6
-0.9428 - 0.158 i
0.226 - 0.067 i
7
1.5047 + 0.455 i
0.0577 - 0.0229 i
8
1.5047 - 0.455 i
0.0577 + 0.0229 i
9
-1.3129 + 0.9839 i
0.112 + 0.301 i
10
-1.3129 - 0.9839 i
0.112 - 0.301 i
11
1.4118 + 1.3185 i
0.00126 + 0.0683 i
12
1.4118 - 1.3185 i
0.00126 - 0.0683 i
13
2.4224 + 1.5637 i
0.149 - 0.0241 i
14
2.4224 - 1.5637 i
0.149 + 0.0241 i
15
7.22 + 4.1367 i
0.332 - 0.219 i
16
7.22 - 4.1367 i
0.332 + 0.219 i
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Table 11. Singularities with their weights for the quadratic approximant [8, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.4946 + 0.e-4 i
0.0136 + 0.0135 i
Singularities of quadratic [8, 8, 8] approximant
2
-0.4946 - 0.e-4 i
0.0136 - 0.0135 i
3
-0.5689 + 0.0714 i
0.382 + 0.279 i
4
-0.5689 - 0.0714 i
0.382 - 0.279 i
5
-0.754
0.461
6
-1.1579
0.166 i
7
-1.5654
0.243
8
1.6094 + 0.2919 i
0.142 + 0.125 i
9
1.6094 - 0.2919 i
0.142 - 0.125 i
10
-1.3779 + 1.2633 i
0.222 - 0.238 i
11
-1.3779 - 1.2633 i
0.222 + 0.238 i
12
1.751 + 0.9901 i
0.108 - 0.0141 i
13
1.751 - 0.9901 i
0.108 + 0.0141 i
14
1.2525 + 2.2552 i
0.0824 - 0.109 i
15
1.2525 - 2.2552 i
0.0824 + 0.109 i
16
14.0509
1.05
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Table 12. Singularities with their weights for the quadratic approximant [9, 8, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.3961 + 0.e-5 i
0.00023 + 0.00023 i
Singularities of quadratic [9, 8, 8] approximant
2
-0.3961 - 0.e-5 i
0.00023 - 0.00023 i
3
-0.5686 + 0.0711 i
0.363 + 0.306 i
4
-0.5686 - 0.0711 i
0.363 - 0.306 i
5
-0.7529
0.47
6
-1.1903
0.147 i
7
-1.5627
0.216
8
1.5899 + 0.2664 i
0.111 + 0.0523 i
9
1.5899 - 0.2664 i
0.111 - 0.0523 i
10
1.6371 + 0.997 i
0.0709 + 0.00318 i
11
1.6371 - 0.997 i
0.0709 - 0.00318 i
12
-1.4358 + 1.431 i
0.00351 + 0.261 i
13
-1.4358 - 1.431 i
0.00351 - 0.261 i
14
0.7679 + 2.0693 i
0.0372 - 0.0289 i
15
0.7679 - 2.0693 i
0.0372 + 0.0289 i
16
0.5179 + 2.7623 i
0.0324 + 0.063 i
17
0.5179 - 2.7623 i
0.0324 - 0.063 i
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Table 13. Singularities with their weights for the quadratic approximant [9, 9, 8]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5688 + 0.0705 i
0.382 + 0.362 i
Singularities of quadratic [9, 9, 8] approximant
2
-0.5688 - 0.0705 i
0.382 - 0.362 i
3
-0.7437
0.572
4
-0.8871 + 0.1947 i
0.135 + 0.0821 i
5
-0.8871 - 0.1947 i
0.135 - 0.0821 i
6
-0.9675 + 0.1479 i
0.0733 - 0.111 i
7
-0.9675 - 0.1479 i
0.0733 + 0.111 i
8
-1.2556
0.541 i
9
1.5416 + 0.4096 i
0.0701 - 0.0509 i
10
1.5416 - 0.4096 i
0.0701 + 0.0509 i
11
-1.3467 + 0.8981 i
0.0743 - 0.443 i
12
-1.3467 - 0.8981 i
0.0743 + 0.443 i
13
1.9564
0.173
14
1.6177 + 1.3319 i
0.00562 + 0.153 i
15
1.6177 - 1.3319 i
0.00562 - 0.153 i
16
2.7348
3.1 i
17
6.832
0.55
18
379.1968
13.5 i
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Table 14. Singularities with their weights for the quadratic approximant [9, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.5687 + 0.0706 i
0.367 + 0.35 i
Singularities of quadratic [9, 9, 9] approximant
2
-0.5687 - 0.0706 i
0.367 - 0.35 i
3
-0.7497
0.491
4
-0.6653 + 0.3642 i
0.00325 + 0.0151 i
5
-0.6653 - 0.3642 i
0.00325 - 0.0151 i
6
-0.6662 + 0.3656 i
0.0151 - 0.00326 i
7
-0.6662 - 0.3656 i
0.0151 + 0.00326 i
8
-1.1995
0.179 i
9
1.6069 + 0.3821 i
0.138 - 0.175 i
10
1.6069 - 0.3821 i
0.138 + 0.175 i
11
-1.7251 + 1.0248 i
4.89 + 3.34 i
12
-1.7251 - 1.0248 i
4.89 - 3.34 i
13
-2.2721
0.43
14
2.3629
0.222
15
1.7181 + 1.7316 i
0.514 + 0.217 i
16
1.7181 - 1.7316 i
0.514 - 0.217 i
17
2.13 + 1.2384 i
0.276 - 0.365 i
18
2.13 - 1.2384 i
0.276 + 0.365 i
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Table 15. Singularities with their weights for the quadratic approximant [10, 9, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.2858
2.22e-7 - 2.22e-7 i
Singularities of quadratic [10, 9, 9] approximant
2
0.2858
2.22e-7 + 2.22e-7 i
3
-0.5691 + 0.0703 i
0.412 + 0.377 i
4
-0.5691 - 0.0703 i
0.412 - 0.377 i
5
-0.7064 + 0.0094 i
0.245 + 0.89 i
6
-0.7064 - 0.0094 i
0.245 - 0.89 i
7
-0.7868
0.479
8
-0.9948
0.539 i
9
-1.5487 + 0.0895 i
0.478 + 0.258 i
10
-1.5487 - 0.0895 i
0.478 - 0.258 i
11
1.5436 + 0.4121 i
0.0684 - 0.041 i
12
1.5436 - 0.4121 i
0.0684 + 0.041 i
13
-1.3548 + 0.9487 i
0.15 + 0.52 i
14
-1.3548 - 0.9487 i
0.15 - 0.52 i
15
1.8158
0.128
16
1.6281 + 1.3784 i
0.0361 - 0.16 i
17
1.6281 - 1.3784 i
0.0361 + 0.16 i
18
2.3149
51.1 i
19
8.1322
0.736
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Table 16. Singularities with their weights for the quadratic approximant [10, 10, 9]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.569 + 0.0703 i
0.403 + 0.374 i
Singularities of quadratic [10, 10, 9] approximant
2
-0.569 - 0.0703 i
0.403 - 0.374 i
3
-0.735 + 0.0077 i
0.136 + 2.36 i
4
-0.735 - 0.0077 i
0.136 - 2.36 i
5
-0.8383
1.14
6
-0.9274
2.91 i
7
1.579 + 0.3699 i
0.0226 - 0.159 i
8
1.579 - 0.3699 i
0.0226 + 0.159 i
9
-1.3837 + 0.8828 i
0.228 - 0.765 i
10
-1.3837 - 0.8828 i
0.228 + 0.765 i
11
-1.7618 + 0.051 i
3.87 - 3.37 i
12
-1.7618 - 0.051 i
3.87 + 3.37 i
13
1.57 + 1.0903 i
0.0447 - 0.0122 i
14
1.57 - 1.0903 i
0.0447 + 0.0122 i
15
1.7257 + 1.2446 i
0.00478 + 0.0468 i
16
1.7257 - 1.2446 i
0.00478 - 0.0468 i
17
1.4274 + 1.6169 i
0.0669 + 0.0397 i
18
1.4274 - 1.6169 i
0.0669 - 0.0397 i
19
-14.1057 + 9.6483 i
0.772 + 0.236 i
20
-14.1057 - 9.6483 i
0.772 - 0.236 i
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Table 17. Singularities with their weights for the quadratic approximant [10, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.569 + 0.0703 i
0.402 + 0.374 i
Singularities of quadratic [10, 10, 10] approximant
2
-0.569 - 0.0703 i
0.402 - 0.374 i
3
-0.7391 + 0.0033 i
3.41 - 5.8 i
4
-0.7391 - 0.0033 i
3.41 + 5.8 i
5
-0.8803 + 0.0125 i
3.95 - 4.94 i
6
-0.8803 - 0.0125 i
3.95 + 4.94 i
7
1.413 + 0.2647 i
0.00922 - 0.001 i
8
1.413 - 0.2647 i
0.00922 + 0.001 i
9
1.4029 + 0.3257 i
0.000638 + 0.00793 i
10
1.4029 - 0.3257 i
0.000638 - 0.00793 i
11
-1.4794
3.35
12
1.4517 + 0.4362 i
0.0151 - 0.00167 i
13
1.4517 - 0.4362 i
0.0151 + 0.00167 i
14
-1.6097
1.97 i
15
-1.3925 + 0.8895 i
0.187 - 0.764 i
16
-1.3925 - 0.8895 i
0.187 + 0.764 i
17
1.5853 + 1.4615 i
0.0996 - 0.0963 i
18
1.5853 - 1.4615 i
0.0996 + 0.0963 i
19
6.4635
0.975
20
-8.0799
0.89
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Table 18. Singularities with their weights for the quadratic approximant [11, 10, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
0.0035
0
Singularities of quadratic [11, 10, 10] approximant
2
0.0035
0
3
-0.569 + 0.0703 i
0.402 + 0.375 i
4
-0.569 - 0.0703 i
0.402 - 0.375 i
5
-0.7345
2.4
6
-0.7468
9.84 i
7
-0.8796 + 0.0348 i
0.639 + 2.16 i
8
-0.8796 - 0.0348 i
0.639 - 2.16 i
9
-1.371 + 0.0232 i
3.5 + 2.83 i
10
-1.371 - 0.0232 i
3.5 - 2.83 i
11
1.5872 + 0.4034 i
0.13 - 0.0911 i
12
1.5872 - 0.4034 i
0.13 + 0.0911 i
13
-1.3751 + 0.9088 i
0.0407 - 0.619 i
14
-1.3751 - 0.9088 i
0.0407 + 0.619 i
15
1.6278 + 1.4739 i
0.153 - 0.181 i
16
1.6278 - 1.4739 i
0.153 + 0.181 i
17
2.2879
0.182
18
2.2092 + 1.0972 i
0.21 + 0.348 i
19
2.2092 - 1.0972 i
0.21 - 0.348 i
20
3.0014
0.462 i
21
123.4717
11.7
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Table 19. Singularities with their weights for the quadratic approximant [11, 11, 10]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.569 + 0.0703 i
0.4 + 0.376 i
Singularities of quadratic [11, 11, 10] approximant
2
-0.569 - 0.0703 i
0.4 - 0.376 i
3
-0.7343
0.812
4
-0.8181 + 0.0531 i
0.234 - 0.103 i
5
-0.8181 - 0.0531 i
0.234 + 0.103 i
6
-0.8193 + 0.1113 i
0.0134 - 0.312 i
7
-0.8193 - 0.1113 i
0.0134 + 0.312 i
8
-1.0454
0.617 i
9
1.0087 + 0.7232 i
0.00116 - 0.00131 i
10
1.0087 - 0.7232 i
0.00116 + 0.00131 i
11
1.0091 + 0.7247 i
0.00131 + 0.00116 i
12
1.0091 - 0.7247 i
0.00131 - 0.00116 i
13
1.5481 + 0.3569 i
0.0143 + 0.0784 i
14
1.5481 - 0.3569 i
0.0143 - 0.0784 i
15
-1.3479 + 0.8999 i
0.177 - 0.463 i
16
-1.3479 - 0.8999 i
0.177 + 0.463 i
17
1.4893 + 1.3976 i
0.031 - 0.0529 i
18
1.4893 - 1.3976 i
0.031 + 0.0529 i
19
-4.1826 + 2.9775 i
0.0588 + 0.318 i
20
-4.1826 - 2.9775 i
0.0588 - 0.318 i
21
-1.8639 + 6.1136 i
0.22 - 0.169 i
22
-1.8639 - 6.1136 i
0.22 + 0.169 i
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Table 20. Singularities with their weights for the quadratic approximant [11, 11, 11]
The most stable singularity is highlighted.
No. zcc Location in the complex plane
1
-0.569 + 0.0703 i
0.401 + 0.374 i
Singularities of quadratic [11, 11, 11] approximant
2
-0.569 - 0.0703 i
0.401 - 0.374 i
3
-0.7363
1.89
4
-0.0172 + 0.7493 i
0.000452 - 0.000237 i
5
-0.0172 - 0.7493 i
0.000452 + 0.000237 i
6
-0.0172 + 0.7493 i
0.000237 + 0.000452 i
7
-0.0172 - 0.7493 i
0.000237 - 0.000452 i
8
-0.7546
4.08 i
9
-0.8747 + 0.0592 i
0.273 + 0.974 i
10
-0.8747 - 0.0592 i
0.273 - 0.974 i
11
-1.3057
0.693
12
-1.5055
0.829 i
13
1.5761 + 0.4007 i
0.103 - 0.0876 i
14
1.5761 - 0.4007 i
0.103 + 0.0876 i
15
-1.409 + 0.8859 i
0.279 - 0.813 i
16
-1.409 - 0.8859 i
0.279 + 0.813 i
17
2.0565
0.217
18
1.6794 + 1.4158 i
0.0383 - 0.25 i
19
1.6794 - 1.4158 i
0.0383 + 0.25 i
20
2.7877 + 1.3879 i
0.555 + 0.338 i
21
2.7877 - 1.3879 i
0.555 - 0.338 i
22
-6.4577
0.891
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ExamplesAr cc-pVDZbh aug-cc-pVQZ 0.9r_ebh aug-cc-pVQZ 1.0r_ebh aug-cc-pVQZ 1.1r_ebh aug-cc-pVQZ 1.2r_ebh aug-cc-pVQZ 1.3r_ebh aug-cc-pVQZ 1.4r_ebh aug-cc-pVQZ 1.5r_ebh aug-cc-pVQZ 1.6r_ebh aug-cc-pVQZ 1.7r_ebh aug-cc-pVQZ 1.8r_ebh aug-cc-pVQZ 1.9r_ebh aug-cc-pVQZ 2.0r_ebh aug-cc-pVQZ 2.1r_ebh aug-cc-pVQZ 2.2r_ebh cc-pvdz 1.5rebh cc-pvdz 2rebh cc-pvdz rebh cc-pvqz 1.5rebh cc-pvqz 2rebh cc-pvqz rebh cc-pvtz 1.5rebh cc-pvtz 2rebh cc-pvtz reh- cc-pv5zh- cc-pvqzhf aug-cc-pVDZ 1.5r_ehf aug-cc-pVDZ 2.0r_ehf aug-cc-pVDZ r_ehf cc-pvdz 1.5rehf cc-pvdz 2rehf cc-pvdz 2rehf cc-pvdz rena-pl aug-cc-pvdzNe cc-pVDZo2- aug-cc-pvdz
MoleculeArX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHX 1^Sigma+ State of BHH- ionH- ionX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFX 1^Sigma+ State of HFNa+NeX 1^Sigma+ State of O2-
Basiscc-pVDZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZAUG-CC-PVQZCC-PVDZCC-PVDZCC-PVDZCC-PVQZCC-PVQZCC-PVQZCC-PVTZCC-PVTZCC-PVTZAUG-CC-PV5ZAUG-CC-PVQZAUG-CC-PVDZAUG-CC-PVDZAUG-CC-PVDZCC-PVDZCC-PVDZCC-PVDZCC-PVDZAUG-CC-PVDZcc-pVDZAUG-CC-PVDZ

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